R Squared - Meaning, Formula and Calculation

Learn all the detail about R Squared– its calculation, interpretation, and real-world applications. Gain insights into leveraging this powerful metric for data analysis and decision-making.
R Squared - Meaning, Formula and Calculation
3 min
28 March 2024

Statistical tools and metrics are important for evaluating different types of investments in the market. One such tool is the R-squared (R2), which many investors often overlook because of its perceived complexity. However, the R-squared in mutual funds and other assets is a fairly simple concept once you have understood what it means.

So, let us examine the meaning and significance of the R-squared metric, how it is calculated and what its limitations are.

R-squared: Definition and significance

In statistical terms, the R-squared (also known as the coefficient of determination) measures the variance in a dependent variable with respect to an independent variable. This tool is developed based on the regression model, which is quite different from the correlation of an asset.

The correlation tells you how strongly one variable depends on another. However, the R-squared evaluates how the variance in one variable can be explained using the variance of another variable. For instance, every mutual fund scheme has a corresponding benchmark. The R-squared of a mutual fund with respect to its benchmark index tells you how much the fund’s performance mirrors the benchmark and is affected by it.

Calculating the R-squared value

The process of calculating the R-squared value for mutual funds and other assets can be quite time-consuming. The formula, as shown below, is quite straightforward. However, finding the metrics used in the formula can be tedious.

R-squared = 1 — (Unexplained variation ÷ Total variation


To calculate the unexplained variation, you need to follow the steps outlined below:

  • Use the data points of the dependent and independent variables to find the line of best fit.
  • Then, find the difference between the predicted values and the actual values.
  • Square the difference obtained above and add all the differences to get the total of errors squared.
  • This is the unexplained variation.

To find the total variation:

  • Find the difference between each actual value and the average value.
  • Square each of the above differences and add them.

Needless to say, this can be prone to errors and time-consuming if you are investing in a volatile market. A better alternative to calculate the R-squared is to use the formula given below in a excel spreadsheet:

R-squared = RSQ ([Data set 1],[Data set 2])


Interpret R-squared values in investing

R-squared is typically expressed as a percentage and its value can range from 0% to 100%. The higher the value, the more the dependent variable’s variation can be explained by the variation of the independent variable.

For instance, take the case of a mutual fund and its benchmark. The fund is the dependent variable here, and the benchmark is the independent variable. A 70% R-squared in the mutual fund means that the benchmark’s variation accounts for only 70% of the mutual fund’s variation. The remaining 30% is due to other non-benchmark-related factors.

How is the value of R-squared in mutual funds useful

The R-squared value can be used to choose the right kind of investment for your portfolio. If you want to mimic the returns or performance of a benchmark index, for instance, you must compare mutual funds and choose those where the R-squared value is very high — preferably 95% or more.

You can find such high R-squared in index funds, which are specifically designed to mimic the movement of the benchmark index. Other funds that are actively managed may have lower R-squared values.

Drawbacks of the R-squared measure

The R-squared values can be useful to measure an asset against its benchmark. However, it falls short in other areas, as outlined below:

  • It relies on historical data, which may not repeat itself.
  • It does not facilitate comparison with other investments.
  • It cannot help you measure the performance of an asset.

Adjusted R-squared: An effective alternative

The R-squared is also limiting because it can only account for one independent variable or benchmark. However, most assets and mutual funds may have more than one benchmark. An adjusted R-squared can help you measure the impact of multiple independent variables or benchmarks on an asset.

To put it simply, the R-squared value always increases when more variables are added. But this increase may not necessarily translate to a rising correlation. An adjusted R-squared, however, can help you figure out the impact of different benchmarks more accurately.

Conclusion

The R-squared is only one of the many factors you need to consider to evaluate an investment. Since the metric does not measure the performance of an asset or its broader market-related risk, you also need to look into other aspects like the asset’s beta, standard deviation and volatility. You can then make a more well-informed decision.

After you have performed the required analysis and identified the funds you want to invest in, you can visit the Bajaj Finserv Mutual Funds Platform and start your lump sum or SIP investment. With over 1,000 funds available to choose from, you are bound to find the funds that align with your risk preferences and financial goals.

Frequently asked questions

What value of R-squared is considered good?

No value of the R-squared can be interpreted as good or bad. This statistical tool does not measure the performance of an asset. It only tells you the extent of variation in the asset for any variation in its benchmark.

Is it better if the R-squared is high?

A high R-squared value does not necessarily mean it is better or worse. It simply indicates that the extent of variation in a security is high for any corresponding variation in the benchmark.

What does it mean if an asset has an R-squared of 0.5?

An R-squared value of 0.5 or 50% means that only half the variation in the asset’s price can be traced back to variation in the benchmark. The other half depends on other unexplained factors.

What does a low R2 value indicate?

A low R-squared value means that only a small part of the extent of variation in the asset can be linked to variation in its benchmark.

What is the meaning of R-squared in mutual funds?

The R-squared in mutual funds indicates how similar or different the performance of the fund is when compared to its benchmark.

What is the R2 of a portfolio?

The R-squared of an investment portfolio measures the extent to which the portfolio varies along with its benchmark. The higher the R-squared value, the more of the portfolio’s variation can be linked to its benchmark.

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